If A = 3i + 6j - 2k, then the unit vector parallel to A will be:
Correct answer: B. (1/7) * (3i + 6j - 2k)
- A. 1/7 (3i + 6j - 2k)
- B. (1/7) * (3i + 6j - 2k)
- C. (1/14) * (3i + 6j - 2k)
- D. 3i + 6j - 2k
- E. 7(3i + 6j - 2k)
Explanation
To find a unit vector parallel to a given vector A = 3i + 6j - 2k, first calculate the magnitude of A: |A| = √(3² + 6² + (-2)²) = √(9 + 36 + 4) = √49 = 7. The unit vector, denoted as û, is then calculated by dividing each component of A by its magnitude: û = (1/7)(3i + 6j - 2k) = (3/7)i + (6/7)j - (2/7)k. Therefore, the correct answer is (1/7) * (3i + 6j - 2k). The other options either use incorrect magnitudes or represent the vector A itself, not the unit vector.
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